Quantum-inspired algorithm for truncated total least squares solution

TL;DR

This paper introduces a quantum-inspired algorithm for efficiently approximating the truncated total least squares solution in large-scale data fitting problems, considering measurement errors in both data and matrix.

Contribution

It presents a novel quantum-inspired approach for TTLS, improving computational efficiency in large-scale ill-posed problems with practical error considerations.

Findings

The algorithm achieves accurate approximations of TTLS solutions.

Numerical experiments demonstrate the method's efficiency.

The approach is suitable for large-scale data fitting problems.

Abstract

Total least squares (TLS) methods have been widely used in data fitting. Compared with the least squares method, for TLS problem we takes into account not only the observation errors, but also the errors in the measurement matrix. This is more realistic in practical applications. For the large-scale discrete ill-posed problem $Ax \approx b$, we introduce the quantum-inspired techniques to approximate the truncated total least squares (TTLS) solution. We analyze the accuracy of the quantum-inspired truncated total least squares algorithm and perform numerical experiments to demonstrate the efficiency of our method.